As foreshadowed by the feel-good lead single "Kodachrome" (which reached #2 on the Billboard charts, blocked by Billy Preston's "Will It Go Round in Circles"), There Goes Rhymin' Simon proved to be a bigger hit than its predecessor, reaching #2 on the Billboard 200 chart (kept off the top spot by George Harrison's Living in the Material World), and #1 on Cashbox Magazine for one week on June 30, 1973.[4] In the United Kingdom, the album peaked at #4. Subsequent singles were also the #2 single "Loves Me Like a Rock" (knocked-off by Cher's "Half-Breed", but reaching #1 on Cashbox on September 29, 1973), and the Top 40 hit "American Tune". Also "Take Me to the Mardi Gras" was released in the UK reaching the Top 20.

The song "Kodachrome" is named after the Kodak film of the same name. Kodak required the album to note that Kodachrome is a trademark of Kodak. The song was not released as a single in Britain, where it could not be played on BBC radio due to its trademarked name. The song "Was a Sunny Day" has an interesting reference to early rock and roll in the line "She called him Speedo but his Christian name was Mr. Earl" which echoes the chorus from the 1955 song "Speedo" by The Cadillacs: "They often call me Speedo but my real name is Mr. Earl," referring to lead singer, Earl "Speedo" Carroll.

Robert Hilburn of the Los Angeles Times said, "Combining a variety of musical textures (from a touch of gospel to an infectious trace of Jamaican rhythm to a hint of the old Simon and Garfunkel grandeur), Simon's new album firmly establishes him as one of our most valuable and accessible artists."[6]

But Stereo Review's Noel Coppage found much to complain about. Though he gave it an "excellent" rating, he added that it was "deficient in spontaneity, excitement, strain...I don't know how it could sound so cut-and-dried, having been recorded in four different locations (New York, London, Muscle Shoals, and Jackson, Mississippi), but although the arrangements are clean and sensible, they are oddly predictable."[7]